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Shock wave solutions of conservation laws and their regularization by dissipation and dispersion.

Series:

PDE Seminar

Tuesday, November 4, 2014 - 15:00

1 hour (actually 50 minutes)

Location:

Skiles 006

Speaker:

Michael Shearer

,

North Carolina State University

Shock waves are idealizations of steep spatial gradients of
physical quantities such as pressure and density in a gas,
or stress in an elastic solid. In this talk, I outline the mathematics
of shock waves for nonlinear partial differential equations
that are simple models of physical systems. I will focus on
non-classical shocks and smooth waves that they approximate. Of particular interest are comparisons between nonlinear traveling
waves influenced strongly by dissipative effects such as viscosity or
surface tension, and spreading waves generated by the balance between dispersion and
nonlinearity, when the nonlinearity is non-convex.